Solving Differential Equations Using Feedforward Neural Networks

Abstract

In this work we explore the use of deep learning models based on deep feedforward neural networks to solve ordinary and partial differential equations. The illustration of this methodology is given by solving a variety of initial and boundary value problems. The numerical results, obtained based on different feedforward neural networks structures, activation functions and minimization methods, were compared to each other and to the exact solutions. The neural network was implemented using the Python language, with the Tensorflow library.